Republican presidential candidate Donald Trump said Wednesday that under his administration there will be no way for those who enter the U.S. illegally to become a citizen.

He gave a detailed rundown of his immigration policy plans to supporters in the southwestern state of Arizona hours after meeting with Mexican President Enrique Pena Nieto.

First on Trump's list was the reiteration of his commitment to construct a wall at the U.S.-Mexico border, and that Mexico will pay pick up the cost, despite Pena Nieto's repeated statements that his government will not.

"They don't know it yet, but they're going to pay for the wall."

Trump asserted the U.S. has the right to pick immigrants who are most likely to "thrive and flourish" and love Americans.

Embed code

Copy and paste the embed code below. The code changes based on your selection.

Share this video

"We also have to be honest about the fact that not everyone who seeks to join our country will be able to successfully assimilate."

Trump described his immigration policies as prioritizing the security and economic well-being of Americans, and said the proposals would bring down crime, gangs, illegal border crossings and welfare use.

"People will know that you can't just smuggle in, hunker down and wait to be legalized," he said.

Trump was more subdued at a news conference in Mexico City after his meeting with the Mexican president, which he described as important and straightforward.

"I love the United States very much and I want to make sure the people of the United States are very protected," Trump told Pena Nieto at a news conference Wednesday in Mexico City. "You equally expressed your feelings and love for Mexico."

Trump won much of his support throughout the campaign with rhetoric that Pena Nieto called hurtful to the Mexican people. Trump has said the United States' southern neighbor steals jobs, sends rapists and criminals and murderers across the border, and does little to stop illegal immigrants. He has insisted Mexico will pay for a wall that he wants built along the border.

But it was a much more subdued and respectful Trump who spoke after meeting with the Mexican president.

Trump said he has a "tremendous feeling" for Mexican Americans, calling them "spectacular, hard-working people" and saying he is proud to employ many in his industries, calling them "beyond reproach."

Trump said he and the president talked about the wall at the border, but not about who would pay for it.

But Pena Nieto, contradicting Trump, later said he told the U.S. businessman that Mexico will not pay for the wall, repeating something he has said numerous times.

Trump did say the North American Free Trade Agreement has been a greater benefit to Mexico than the United States. He said the 22-year-old deal needs to be updated to reflect "today's realities."

He also said all countries have a sovereign right to a secure border, including building walls, and that illegal immigration from Central America through Mexico and into the U.S. is a humanitarian disaster.

WATCH: Trump Discusses Mexican Americans, Border Crossings

Embed code

Copy and paste the embed code below. The code changes based on your selection.

Share this video

Trump said cartels and other criminal gangs that terrorize northern Mexico can be wiped out only through intelligence sharing and joint operations.

"The bond between our two countries is deep and sincere, and both our nations benefit from close and honest relations ... a strong Mexico is in the best interest of the United States," Trump said.

Pena Nieto spoke directly to Trump at the news conference, saying his priority is protecting Mexicans wherever they may be. He said Mexicans living in the U.S. are creative and talented and honest working people who respect family, their communities and the law. He said they deserve everyone's respect in return.

Pena Nieto called the border an asset for both countries, and said that 1 million people cross it every day. He said Americans who see the border as a problem that brings in drugs and illegal immigrants are getting an "incomplete picture." He said the U.S. must do what it can to stop weapons and cash from flowing into Mexico to the drug cartels.

Trump had announced his hastily planned visit to Mexico City just days after the Mexican leader extended the invitation to him and to his Democratic opponent, former U.S. Secretary of State Hillary Clinton.

Demonstrators hold placards during a protest against the visit of U.S. Republican presidential candidate Donald Trump at the Angel of Independence monument in Mexico City, Mexico, Aug. 31, 2016.

Pena Nieto drew criticism for his meeting with Trump, who is widely reviled in Mexico. Former President Vicente Fox told CNN that he does not understand why Pena Nieto extended the invitation, saying, "He [Trump] is not welcome to Mexico. He is going to be rejected by everybody here."

A few dozen demonstrators gathered Wednesday in the center of the capital to protest the visit, some holding signs that read "You are not Wall-come" and "Trump and Pena out."

Trump's visit came hours before he plans to unveil his new immigration policies during a campaign speech in the border state of Arizona. Trump has said he could "soften" his hard-line proposal to create a "deportation force" to send 11 million undocumented immigrants in the U.S. back home.

Pena Nieto said he hopes Clinton also will accept his invitation to meet in Mexico City.